Emerging from a White House meeting with President Obama on Monday, Sen. John McCain, R-Ariz., said it would be "catastrophic" for Congress to reject the president's request to take military action against Syria's use of chemical weapons, but that the administration needs to outline a stronger case to the American people.

"If the Congress were to reject a resolution like this after the President of the United States has already committed to action, the consequences would be catastrophic in that the credibility of this country, with friends and adversaries alike, would be shredded and there would be not only implications for this presidency, but for future presidencies as well," McCain told reporters shortly after meeting with the president in the Oval Office.

Sen. Lindsey Graham, R-S.C., who along with McCain, met with Obama for roughly an hour, was optimistic that the administration is developing a comprehensive military strategy -- a "pretty solid plan" -- but said he needs to see more details.

"For the first time, I see the development of a strategy that will upgrade the opposition as well as degrade Assad," said Graham, who urged the president to "up his game" in explaining the need for action to the "skeptical" American public.

McCain added: "Tell us without any hesitation, Mr. President, what does it matter to us as a nation if this war goes on and Assad wins?"

"I believe the president is capable of doing that, has not yet done it, but he is ready to do it. And if he's ready to do that part, I'm ready to go to my colleagues in the Congress and say, 'Now's the time for us to come together before it's too late.'"

By extending an invitation to McCain to visit the White House this afternoon, the administration is hoping the president's one-time foe will become a crucial ally to help convince skeptical lawmakers on both sides of the aisle to vote for military intervention in Syria.

After the president announced Saturday that he will seek congressional approval for any military strikes in Syria, Graham and McCain, both foreign policy hawks, could be important pieces to the puzzle as the administration tries to rally support for military action against Syria among war-weary lawmakers and the nation.

Congress will not vote on the war resolution until at least the week of Sept. 9, when both chambers return for legislation business, giving the White House a short opportunity to build the president's argument that the Syrian government's use of chemical weapons on its own people merits a U.S. military strike.

Obama's decision to seek congressional authority sets the stage for the biggest foreign policy vote in Congress since the Iraq war.

McCain, who traveled to Syria in May to meet with rebel forces, and Graham support military action in Syria, but they don't think the president's plans go far enough and are calling for more than just isolated strikes.

"Rather than just we're going to launch some cruise missiles and -- and that's it -- and even worry more when the president's chief of staff -- chairman of the Joint Chiefs -- says, 'Well, it doesn't matter when we strike.' Well, that's not a military action then. That's a symbolic action. So we need to have a strategy and a plan, and that plan, in our view -- the best way to eliminate the threat of Bashar Assad's continued use of chemical weapons -- and, by the way, we know he's used them a number of times before -- would be the threat of his removal from power," McCain said.

Despite his criticism, McCain did signal a possible willingness to support the president, acknowledging that the "consequences of the Congress of the United States overriding a decision of the president of the United States of this magnitude are really very, very serious.

"And, already, we're sending a bad signal to Iran, to North Korea, to Bashar Assad," although he did not confirm a vote, saying he first needs to see a "strategy" that military action "will achieve some goals that we need to achieve."

"We have to have a plan. It has to be a strategy. It can't just be, in my view, pinprick cruise missiles," McCain said, echoing what he and Graham said in a statement this weekend, which said while they support military intervention they "cannot in good conscience support isolated military strikes in Syria that are not part of an overall strategy that can change the momentum on the battlefield, achieve the President's stated goal of Assad's removal from power, and bring an end to this conflict, which is a growing threat to our national security interests."

Of course, there are many other lawmakers, a bipartisan group of both Republicans and Democrats, who disagree with McCain, as well as the president, and don't want to see military action at all. In talking to lawmakers Sunday, several intimated to ABC News that they believe it would fail.

"I'm not there yet," Rep. Janice Hahn, D-Calif., said after the briefing. "I am hoping to find an answer to the question, is there another way to hold Assad accountable?"

Rep. Elijah Cummings, D-Md., added, "There's a lot more questions I have to have answered. I want to know exactly what the game plan is."

The president, as well as Secretary of State John Kerry, have said while the president is seeking authorization from Congress, he has the power to act even if the vote fails.

Many members Sunday complained that the administration's resolution is too broad and gives the president too much discretion for what has been described as a "limited" and "narrow" strike.

"The biggest single concern among the members may very well have been a very broad request for authority with supposedly a very narrow intent to do anything and I think that has to be narrowed down in the next week," Sen. Roy Blunt, R-Mo., said.

"At the same time, the limited willingness to do anything that would actually change events on the ground except discourage further use of chemical weapons is something that members, including me, are going to have to deal with whether or not that limited effort is worth the next step."

Blunt said that new language is more than likely to come about before Congress takes the vote.

"The administration is open on the language issue and I think they will have to be if they want to get their language through Congress," Blunt said.

The administration's efforts continue Tuesday when Kerry and Secretary of Defense Chuck Hagel will testify at a Senate Foreign Relations Committee hearing, a Senate aide confirmed.